If a vector `vecA` makes an angles `alpha, beta and gamma` respectively with the x, y and z axes respectively. Then `sin^(2)alpha + sin^(2)beta + sin^(2)gamma` is equal to

Options

A. 1
B. 2
C. 3
D. none of these

Answer

B

Explanation

We have
`l=cos alpha, m=cos beta` and `n=cos gamma`
`:.l^(2)+m^(2)+n^(2)=1`
`impliescos^(2)alpha+cos^(2)beta+cos^(2)gamma=1`
`implies1-sin^(2)alpha+sin^(2)beta+1-sin^(2)gamma=1`
`impliessin^(2)alpha+sin^(2)beta+sin^(2)gamma=2`